Replacement policies for a parallel system with shortage and excess costs

Abstract

It has been assumed in most maintenance models that (i) the number of units for a parallel system can be predefined precisely, (ii) maintenance cost after failure should be avoided, and (iii) age replacement can always be performed at its optimized times. However, these assumptions are challenged from practical perspectives in this paper. For this purpose, shortage and excess costs, which claim that replacement done too early before failure involves a waste of operation, are introduced into replacement models, such as replacement plans with time T or distribution G(t) for constant n or random N of units. Furthermore, the number N of working times and the number n of available units for a scheduled replacement time T are discussed. For each model, the expected replacement cost for one cycle and expected replacement cost rate for a long run are optimized, and numerical examples are given.